Solving by Combining Like Terms
3X + 4 = 2X + 9
|𝑥| = 15
X=15, X= -15
WRITE AN EQUATION & SOLVE: Julie is 3 years older than her sister. Julie's age is 11 years old. How old is her sister?
You must write the equation and the solution.
n - Julie's sister's age n + 3 = 11 n = 8 Julie's sister is 8 years old.
1/3x+1/2x=10/3
x=4
5x - 7 = 3x + 9
x= 8
|𝑥| + 6 = 1
No solution
Mr. Cushman bought 7 Hannah Montana t-shirts for a total of $90.93. Each t-shirt cost the same amount. How many Hannah Montana t-shirts did Mr. Cushman buy?
You must write the equation and the solution.
n - # of t-shirts 7n = 90.93 n = 12.99 Each t-shirt cost $12.99
x/2+x/3=30
x=6
2X+4x-6<18
X < 4
4(x-3)+2>10
X>5
4(x - 2) + 5 = 2x + 3(x+1)
|𝑥 + 1| + 2 = 10
X= 7 X=-9
Tyler has 4 boxes of apples. Each box has the same number of apples. After Tyler eats 3 apples, there are 109 apples left in the boxes. How many apples were in each box?
You must write the equation and the solution.
a - # of apples in each box 4a - 3 = 109 a = 28 There were 28 apples in each box.
1/2x+3=10
x=14
-2(3X-4)<10
x >-1/3
3(2x-1)>5x+7
X>10
4|2𝑥 + 7| = 28
X= 0, X= -7
Mr. Bucci goes to the grocery store and purchases 17 bags of raisins and a $2.97 jar of peanut butter. His total cost was $34.76. What was the cost for a bag of raisins?
You must write the equation and the solution.
r - cost of a bag of raisins 17r + 2.97 = 34.76 r = 1.87 Each bag of raisins cost $1.87
2/3x+3+1/2x=-3
x=-3
-4(x-2)+3x<8x+6
2/9 < x OR x >2/9
−3 + 10|𝑥 − 4| = 47
X= 9, X= -1
When you count by ones from any integer, you are counting consecutive integers. Using variables, three consecutive integers are n, n + 1, and n + 2. The sum of three consecutive integers is 48. What are the three integers?
n + n + 1 + n + 2 = 48 n = 15
The integers are 15, 16, and 17.
1/2y+1/3=2-1/6y
y=5/2